There are no 𝑄-points in Laver’s model for the Borel conjecture

There are no $Q$-points in Laver’s model for the Borel conjecture
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by Arnold W. Miller PDF

Proc. Amer. Math. Soc. 78 (1980), 103-106 Request permission

It is shown that it is consistent with ZFC that no nonprincipal ultrafilter on $\omega$ is a Q-point (also called a rare ultrafilter).

References

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P pt’s in random real extensions

Richard Laver, On the consistency of Borel’s conjecture, Acta Math. 137 (1976), no. 3-4, 151–169. MR 422027, DOI 10.1007/BF02392416
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A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), no. 1, 59–111. MR 491197, DOI 10.1016/0003-4843(77)90006-7

and the P-point problem

P-pts in iterated forcing extensions

Edward L. Wimmers, The Shelah $P$-point independence theorem, Israel J. Math. 43 (1982), no. 1, 28–48. MR 728877, DOI 10.1007/BF02761683